The PT4115 you chose looks like a good choice.

The PT4115 datasheet, page 13, provides information on diode D selection. It is a Schottky diode that should be compatible with the LED operating conditions. The maximum LED operating conditions we find in the LED datasheet are: https://www.ledsupply.com/content/pdf/XLampXML_Color.pdf

From the PT4115 and LED datasheet I derive these diode parameters:
Type: Schottky
Package SMD
Vr >> 6V (DC reverse voltage)
IO >> 1.2A (average rectified current)
Capacitance <?

Searching at Digikey I zeroed in on the onsemi SS3003CH-TL-W with these specs:
https://www.onsemi.com/download/data-sheet/pdf/ss3003ch-d.pdf

Type: Schottky
Package SOT-23-6
Vr >> 30V (DC reverse voltage)
IO >> 3A (average rectified current)
Capacitance 880 pF

PT4115 Datasheet page 13, Diode selection For maximum efficiency and performance, the rectifier (D1) should be a fast low capacitance Schottky diode with low reverse leakage at the maximum operating voltage and temperature. They also provide better efficiency than silicon diodes, due to a combination of lower forward voltage and reduced recovery time. It is important to select parts with a peak current rating above the peak coil current and a continuous current rating higher than the maximum output load current. It is very important to consider the reverse leakage of the diode when operating above 85°C. Excess leakage will increase the power dissipation in the device and if close to the load may create a thermal runaway condition.

LED SPECS


PT4115 SPECS


DIODE SPECS

 

I am first trying out a MOSFET and resistor based solution. Here is my circuit and it works.

Here is the MOSFET datasheet:
https://www.mouser.com/datasheet/2/196/Infineon_IRLB8721_DataSheet_v01_01_EN-3363432.pdf

 

Your schematic is missing the LED dropping resistor...I hope your test circuit isn't missing the resistor.

 

Your schematic is missing the LED dropping resistor...I hope your test circuit isn't missing the resistor.

I don't have a LED dropping resistor aka current-limiting resistor because:

1) I am using a benchtop power supply.
2) I set the power supply voltage to match the forward voltage of the LED. I am providing the exact voltage required for the LED to turn on.
3) I also set the current limit on the power supply to 930mA. This will limiting the amount of current that can flow through the LED. ( The LED Max Forward current is 1 Amp ).

 

LEDs do not work that way. The forward voltage is only specified as a range. Typical range for a white LED 3.2 to 3.6V. As the temperature rises, the forward voltage goes down. For LEDs in the range if 1A, a constant current supply is highly recommended.

Does your power supply have a meter or display for current? If so, what current does it show when you supply 3V? It would be a very unusual white LED if it draws 1A at 3V.

 

LEDs do not work that way. The forward voltage is only specified as a range. Typical range for a white LED 3.2 to 3.6V. As the temperature rises, the forward voltage goes down. For LEDs in the range if 1A, a constant current supply is highly recommended.

Does your power supply have a meter or display for current? If so, what current does it show when you supply 3V? It would be a very unusual white LED if it draws 1A at 3V.

Yes, my power supply has a display for current.
When I supply 3 volts, the current maxed out at 1 Amp. The C.C. light turned on the power supply.
This is a RED led that I was powering.

When I supply 3 volts, the current draw was 17 milli Amps. The C.V. light turned on the power supply.
This is a WHITE led that I was powering.

 

That is about what I would expect.

So, do you see why supplying 3V is not the correct way to drive either of those LEDs?